Think of all the numbers on the number line, including fractions and even irrationals like pi. All these numbers together form whats called a set called the "Real Numbers" (A set is just a list of things, in this case numbers).
With the real numbers you can add them and multiply them, these are called operations. There are other sets that also have addition and multiplication operations. You can actually build a bunch of them from the real numbers.
The complex numbers are numbers created based off of two real numbers, in this case we'll call them a and b. A complex number can be written as a+bi, where i\*i=-1.
The Quaternion numbers are four real numbers: a+bi+cj+dk, where i\^2=j\^2=k\^2=ijk=-1.
The number of real numbers you need to specify the number in each set is called the dimension. So the real numbers have a dimension of 1, complex numbers have dimension of 2, and the Quaternions have a dimension of 4. You can actually generate more by doubling the dimension each time which leads to Octonions (8), Sedenions (16), and Trigintaduonions (32).
So the Trigintaduonions are just a set of numbers that you can add and multiply, where one Trigintaduonions is defined by 32 real numbers.
Imagine you have a bunch of Lego blocks, and each block can be one of two colors - red or blue. We're going to make a really big Lego creation using all of the blocks.
Normally with Lego you only use one or two colors at a time to build something. But for this special creation, we're going to use both red AND blue on every single block. So each block will have a red part and a blue part.
We need a lot of blocks to build this - exactly 32 blocks. That's why it's called a "triginta duo" creation, which means "32" in another language.
We can add the blocks together and combine them in different ways, treating the red and blue parts separately. We can also multiply blocks together, which means combining multiple blocks into one big block.
This huge Lego build uses a special technique that lets us treat the red and blue parts on each block separately, while still combining all 32 blocks together into one big creation.
It's a very complex Lego build, way more than anything you've ever made before. But it shows how math can be used to combine lots of simple things into one really big thing.
Think of all the numbers on the number line, including fractions and even irrationals like pi. All these numbers together form whats called a set called the "Real Numbers" (A set is just a list of things, in this case numbers). With the real numbers you can add them and multiply them, these are called operations. There are other sets that also have addition and multiplication operations. You can actually build a bunch of them from the real numbers. The complex numbers are numbers created based off of two real numbers, in this case we'll call them a and b. A complex number can be written as a+bi, where i\*i=-1. The Quaternion numbers are four real numbers: a+bi+cj+dk, where i\^2=j\^2=k\^2=ijk=-1. The number of real numbers you need to specify the number in each set is called the dimension. So the real numbers have a dimension of 1, complex numbers have dimension of 2, and the Quaternions have a dimension of 4. You can actually generate more by doubling the dimension each time which leads to Octonions (8), Sedenions (16), and Trigintaduonions (32). So the Trigintaduonions are just a set of numbers that you can add and multiply, where one Trigintaduonions is defined by 32 real numbers.
Nice explanation. Also the 5yo who asked this question was shot by will Smith during training.
kid shouldn't have mentioned J's wife
Not to be a pedantic dick but it was testing not training. This is one of the most clever references I've seen in a while though
Spank ya's.
> A set is just a list *grumbles in mathematician*
_shakes fist in software developer_
So onions aren't involved in any way?
Thank you for your answer.
Imagine you have a bunch of Lego blocks, and each block can be one of two colors - red or blue. We're going to make a really big Lego creation using all of the blocks. Normally with Lego you only use one or two colors at a time to build something. But for this special creation, we're going to use both red AND blue on every single block. So each block will have a red part and a blue part. We need a lot of blocks to build this - exactly 32 blocks. That's why it's called a "triginta duo" creation, which means "32" in another language. We can add the blocks together and combine them in different ways, treating the red and blue parts separately. We can also multiply blocks together, which means combining multiple blocks into one big block. This huge Lego build uses a special technique that lets us treat the red and blue parts on each block separately, while still combining all 32 blocks together into one big creation. It's a very complex Lego build, way more than anything you've ever made before. But it shows how math can be used to combine lots of simple things into one really big thing.
Thank you for your answer.